Chapter 1, Problem 1RE

$\text{ Solve }2x+3=7x-11.$

To determine

To calculate: The solution of the linear equation $2x+3=7x-11$ and also check the solution.

Answer to Problem 1RE

The solution of given linear equation is $x=\frac{14}{5}$.

Explanation of Solution

Calculation:

Consider the provided linear equation.

$2x+3=7x-11$

Combine the like terms by adding $-2x$ on both the sides,

$\begin{array}{c}2x+3+\left(-2x\right)=7x-11+\left(-2x\right)\\ 3=5x-11\end{array}$

Now, add $11$ on both the sides,

$\begin{array}{c}3+\left(11\right)=5x-11+\left(11\right)\\ 14=5x\end{array}$

Now, rearrange and divide both sides by $5$,

$\begin{array}{c}5x=14\\ x=\frac{14}{5}\end{array}$

Check

Put $x=\frac{14}{5}$ in the given equation,

$\begin{array}{l}2\left(\frac{14}{5}\right)+3\stackrel{?}{=}7\left(\frac{14}{5}\right)-11\\ \frac{28}{5}+3\stackrel{?}{=}\frac{98}{5}-11\\ \frac{28+15}{5}\stackrel{?}{=}\frac{98-55}{5}\\ \frac{43}{5}=\frac{43}{5}\end{array}$

So, the value of $x$ is true.

Hence, the solution of the given linear equation is $x=\frac{14}{5}$.